Active control systems are often used to suppress noise and/or vibration in certain structures. For example, aboard aerospace structures, noise and vibration reduction can be achieved using compact, surface-mounted piezoelectric actuators. As will be understood by those of ordinary skill in the art, the term “piezoelectric” generally describes the natural capability of certain classes of crystalline materials, e.g., quartz, tourmaline, lead zirconate titanates, barium titanate, etc., to produce a proportional voltage in response to an applied mechanical force or pressure. Piezoelectric materials can also change their shape and/or dimensions in response to an applied electric field, thereby making piezoelectric materials potentially useful as actuators in a host of different applications.
In one particularly simple and robust vibration control strategy referred to as “active damping,” the output of a velocity sensor is fed back to a point force actuator via a fixed control gain. The control approach is guaranteed to be stable for any value of the control gain if the actuator and sensor are matched. However, actuator/sensor pairs in actuality are never perfectly matched, thus necessitating the limitation of any applied control gain to minimize spillover and other system stability issues. Often, an electromagnetic shaker can be used to generate a point force while the integrated response from an accelerometer is used to measure velocity. While the transducers may not be perfectly matched, they are often adequate for vibration control applications. Unfortunately, shakers tend to be large, bulky, and require an inertial base from or against which to react.
Due to the severe space and weight constraints associated with many applications, and in aerospace applications in particular, considerable research has focused on piezoelectric patch actuators, which are compact and can be integrated into the structure. For instance, in U.S. Pat. No. 4,849,668 to Crawley et al., a laminate structural member is provided having embedded piezoelectric elements for sensing and control. Similarly, U.S. Pat. No. 4,565,940 to Hubbard Jr. describes a method for using piezoelectric film to control or damp vibrations in mechanical systems.
Other work has explored the advantages of spatially weighting distributed transducers. For instance, U.S. Pat. No. 5,054,323 of Hubbard Jr., et al. utilizes multiple triangularly-shaped segmented electrodes to characterize the pressure distribution on a rigid surface. By shaping a distributed transducer, researchers are able to vary how the device couples to the structural response. For instance, a triangular shape has been shown to couple to the flexural response of a cantilevered beam in exactly the same way as a point load or sensor applied at the tip of the transducer. However, this result has not been extended to two-dimensional structures such as plates.
Research pertaining to shaped piezoelectric transducers has established that the Laplacian of the spatial distribution determines how the transducer couples to the flexural response of a given structure. Generally triangular-shaped piezoelectric actuators have been demonstrated as capable of producing transverse point forces at each vertex of the actuator, and bending moments along each edge of the actuator. If the base edge of the actuator is aligned along a fixed boundary of a panel structure, then the point forces or loads and the line moment along the base of the actuator do not couple to the structural response. Therefore, a single point sensor that is positioned at a vertex of the actuator opposite the base edge can yield a substantially, although not perfectly, matched sensor/actuator pair. However, line moments created along the lateral edges of the actuator can cause undesirable high-frequency phase problems, which in turn can destabilize certain control methodologies such as negative rate-feedback control.